UNIVERSITY OF TEHRAN
Electrical and Computer Engineering Department
Digital Logic Design, ECE 367, ECE 894, Spring 1401-02
Homework 1
Number representation
Name:
Date:
Username:
1. Assuming the numbers below are in 8-bit 2’s complement system, write their decimal
equivalents.
a.
b.
c.
d.
10110011
11010110
01011000
10111100
2. Assuming the numbers below are in 8-bit Sign and Magnitude system, write their decimal
equivalents.
a.
b.
c.
d.
10110011
11010110
01011000
10111100
3. Numbers below are in 8-bit Sign and Magnitude binary system. Perform the operations
shown. If more bits are needed to represent the result, extend the results to 16 bits.
a.
b.
c.
d.
10110011 + 11010110
01011000 – 10111100
10011010 + 10011001
10100011 – 01110011
4. Numbers below are in 8-bit 2’s complement. Perform operations shown. Indicate if overflow
occurs and show remedy for the overflow.
a.
b.
c.
d.
10110011 + 11010110
01011000 – 10111100
10011010 + 10011001
10100011 – 01110011
5. The following are fixed-point 16-bit unsigned numbers that consist of 8 integer and 8
fractional bits. Show the decimal equivalent of these numbers.
1
a.
b.
c.
d.
1011001111010110
0101100010101000
1001101010010000
1010001101110000
6. The following are fixed-point 16-bit unsigned numbers that consist of 8 integer and 8
fractional bits. Show the decimal equivalent of these numbers.
a.
b.
c.
d.
42.267
241.86
134.001
14.12
2